Calculate Total Cost And Per-Unit Cost © Dale R. Geiger 20111
How does total cost change as level of activity changes? © Dale R. Geiger 20112
Terminal Learning Objective Task: Calculate Total Cost And Per-Unit Cost For A Given Production Volume Condition: You are a cost advisor technician with access to all regulations/course handouts, and awareness of Operational Environment (OE)/Contemporary Operational Environment (COE) variables and actors. Standard: With at least 80% accuracy: Differentiate between fixed and variable costs Express total and per-unit variable cost in an equation Graph total and per-unit variable cost Express total and per-unit fixed costs in an equation Graph total and per-unit fixed costs © Dale R. Geiger 20113
Why Study Cost Relationships? Understanding what drives cost helps to understand how to reduce cost Recognizing cost relationships helps to define what views of cost are useful © Dale R. Geiger 20114
What is Cost Relationship? Describes the change in cost that occurs with a change in a variable Examples: As number of students in class increases, total cost of class increases As snowfall increases, cost of snow removal increases As number of miles driven increases, total cost of trip increases © Dale R. Geiger 20115
What is Cost Expression? Communicates a cost relationship using verbal, numerical and mathematical symbols Use plain language rather than variables x, y, z, etc. Use math symbols Add (+) Subtract (–) Multiply (*) Divide (/) Example: Cost of hotel stay = Cost per day * # of days © Dale R. Geiger 20116
Which Cost Expression is Useful? Sometimes it is useful to know Total Cost Relevant cost of all inputs required to achieve desired output Example: Cost of PCAM = instructor pay + course materials + classroom facilities + students’ pay Sometimes it is useful to know Unit Cost Unit cost = Total cost / # units Example: Cost to train one student © Dale R. Geiger 20117
Linear Cost Relationships The simplest cost relationships can be represented by a straight line Variable Costs Variable Costs - Costs that increase in direct proportion with the volume produced or consumed Total variable cost = Upward sloping line Unit variable cost = Horizontal line Example: Cost of materials used increases in direct proportion to number of units produced © Dale R. Geiger 20118
Variable Cost Expression Total Variable Cost = Variable $Cost per Unit * # Units Variable $Cost per Unit = Sum of all Variable inputs © Dale R. Geiger 20119
Variable Cost Expression Total Variable Cost = Variable $Cost per Unit * # Units Variable $Cost per Unit = Sum of all Variable inputs © Dale R. Geiger
Variable Cost Example The Smoky Mountain Inn Bed and Breakfast reports the following cost information: Depreciation on building$60,000 per year Maintenance person’s salary $30,000 per year Cleaning person’s salary $24,000 per year Real estate taxes $10,000 per year Laundry service $4.00 per person per night Food $6.00 per person per night What is the unit of output? Which costs will change as output changes? What is the cost expression for variable cost per unit? For Total Variable Cost? © Dale R. Geiger
Variable Cost Example © Dale R. Geiger
Variable Cost Example © Dale R. Geiger
Variable Cost Example What is the cost expression for variable cost per person per night? $4 laundry + $6 food = $10 per person/night What is the cost expression for Total variable cost? $10 per person per night * # person/nights © Dale R. Geiger
Variable Cost Example What is the cost expression for variable cost per person per night? $4 laundry + $6 food = $10 per person-night What is the cost expression for Total variable cost? $10 per person per night * # person-night © Dale R. Geiger
Check on Learning What is the definition of a variable cost? What is the generic cost expression for total variable cost? © Dale R. Geiger
Graph of Total Variable Cost $ X Axis = Number of units As # units increases, total variable cost increases © Dale R. Geiger
Graph of Total Variable Cost $ X Axis = Number of units As # units increases, total variable cost increases At 10 units, Cost is $100 © Dale R. Geiger
Graph of Total Variable Cost $ X Axis = Number of units As # units increases, total variable cost increases At 40 units, Cost is $400 © Dale R. Geiger
Graph of Total Variable Cost $ X Axis = Number of units As # units increases, total variable cost increases At 75 units, Cost is $ © Dale R. Geiger
Graph of Unit Variable Cost $ Unit Cost = Total Variable Cost/# Units Unit cost at 10 units = $100/10 units or $10 per unit Unit cost at 10 units = $100/10 units or $10 per unit X Axis = Number of units As # units increases, Unit variable cost remains the same © Dale R. Geiger
Graph of Unit Variable Cost $ Unit cost at 40 units = $400/40 units or $10 per unit Unit cost at 40 units = $400/40 units or $10 per unit X Axis = Number of units As # units increases, Unit variable cost remains the same Unit Cost = Total Variable Cost/# Units © Dale R. Geiger
Graph of Unit Variable Cost $ Unit cost at 75 units = $750/75 units or $10 per unit Unit cost at 75 units = $750/75 units or $10 per unit X Axis = Number of units As # units increases, Unit variable cost remains the same Unit Cost = Total Variable Cost/# Units © Dale R. Geiger
Check on Learning How is Total variable cost represented on the graph? What is the generic cost expression for Variable cost per unit? © Dale R. Geiger
Linear Cost Relationships Fixed Costs Fixed Costs - Costs that do not change with the volume produced or consumed Total fixed cost = Horizontal line Unit Fixed Cost is non-linear Example: The cost of the instructor remains the same regardless of the number of students in the class © Dale R. Geiger
Fixed Cost Expression Total Fixed $Cost = Sum of all Fixed Inputs Fixed $Cost per Unit = Total Fixed $Cost / # Units © Dale R. Geiger
Fixed Cost Expression Total Fixed $Cost = Sum of all Fixed Inputs Fixed $Cost per Unit = Total Fixed $Cost / # Units © Dale R. Geiger
Fixed Cost Example The Smoky Mountain Inn Bed and Breakfast reports the following cost information: Depreciation on building$60,000 per year Maintenance person’s salary $30,000 per year Cleaning person’s salary $24,000 per year Real estate taxes $10,000 per year Laundry service $4.00 per person per night Food $6.00 per person per night What is the unit of output? Which costs will NOT change as output changes? What is the cost expression for Total Fixed Cost? For Fixed Cost per Unit? © Dale R. Geiger
Fixed Cost Example © Dale R. Geiger
Fixed Cost Example © Dale R. Geiger
Fixed Cost Example What is the cost expression for Total Fixed Cost? $60,000 depreciation + $30,000 maintenance salary + $24,000 cleaning salary + $10,000 taxes = $124,000 What is the cost expression for Fixed Cost per Unit? $124,000 / # person/nights © Dale R. Geiger
Fixed Cost Example What is the cost expression for Total Fixed Cost? $60,000 depreciation + $30,000 maintenance salary + $24,000 cleaning salary + $10,000 taxes = $124,000 What is the cost expression for Fixed Cost per Unit? $124,000 / # person-nights © Dale R. Geiger
Check on Learning What is the definition of a fixed cost? What is the generic cost expression for fixed cost per unit? © Dale R. Geiger
Graph of Total Fixed Cost At 10 units, Total Fixed Cost is $124,000 X Axis = Number of units As # units increases, Total Fixed cost remains the same © Dale R. Geiger
Graph of Total Fixed Cost At 40 units, Total Fixed Cost is $124,000 X Axis = Number of units As # units increases, Total Fixed cost remains the same © Dale R. Geiger
Graph of Total Fixed Cost At 75 units, Total Fixed Cost is $124,000 X Axis = Number of units As # units increases, Total Fixed cost remains the same © Dale R. Geiger
Graph of Unit Fixed Cost Unit Cost = Total Fixed Cost/# Units X Axis = Number of units As # units increases, Unit Fixed cost decreases At 10 units, Unit Fixed Cost = $124,000/10 units or $12,400 per unit $12,400 © Dale R. Geiger
Graph of Unit Fixed Cost Unit Cost = Total Fixed Cost/# Units X Axis = Number of units As # units increases, Unit Fixed cost decreases At 40 units, Unit Fixed Cost = $124,000/40 units or $3,100 per unit $3,100 © Dale R. Geiger
Graph of Unit Fixed Cost Unit Cost = Total Fixed Cost/# Units X Axis = Number of units As # units increases, Unit Fixed cost decreases At 75 units, Unit Fixed Cost = $124,000/75 units or $1,653 per unit $1,653 © Dale R. Geiger
Check on Learning How is Total fixed cost represented on the graph? How is Unit fixed cost represented on the graph? © Dale R. Geiger
Demonstration Problem A vehicle repair shop incurs an average parts cost per repair of $220. Shop rent is $5,000 per month. Staff salaries are $5,000 per month and technicians earn a commission on repairs that averages $200 per repair. Which costs are fixed? Which are variable? What is total cost of 100 repairs? 200 repairs? What is unit cost for 100 repairs? 200 repairs? © Dale R. Geiger
Demonstration Problem A vehicle repair shop incurs an average parts cost per repair of $220. Shop rent is $5,000 per month. Staff salaries are $5,000 per month and technicians earn a commission on repairs that averages $200 per repair. Which costs are fixed? Shop Rent $5,000 Staff Salaries 5,000 Total Fixed$10,000 © Dale R. Geiger
Demonstration Problem A vehicle repair shop incurs an average parts cost per repair of $220. Shop rent is $5,000 per month. Staff salaries are $5,000 per month and technicians earn a commission on repairs that averages $200 per repair. Which costs are variable? Parts per repair$220 Commission per repair 200 Total$420 © Dale R. Geiger
Demonstration Problem A vehicle repair shop incurs an average parts cost per repair of $220. Shop rent is $5,000 per month. Staff salaries are $5,000 per month and technicians earn a commission on repairs that averages $200 per repair. What is total cost of 100 repairs? 200 repairs? Total cost= $420 per repair * # repairs + $10,000 $420 per repair*100 repairs+$10,000 = $52,000 $420 per repair*200 repairs+$10,000 = $85,000 © Dale R. Geiger
Demonstration Problem A vehicle repair shop incurs an average parts cost per repair of $220. Shop rent is $5,000 per month. Staff salaries are $5,000 per month and technicians earn a commission on repairs that averages $200 per repair. What is total cost of 100 repairs? 200 repairs? Total cost= $420 per repair * # repairs + $10,000 $420 per repair*100 repairs+$10,000 = $52,000 $420 per repair*200 repairs+$10,000 = $85,000 © Dale R. Geiger
Demonstration Problem A vehicle repair shop incurs an average parts cost per repair of $220. Shop rent is $5,000 per month. Staff salaries are $5,000 per month and technicians earn a commission on repairs that averages $200 per repair. What is total cost of 100 repairs? 200 repairs? Total cost= $420 per repair * # repairs + $10,000 $420 per repair*100 repairs+$10,000 = $52,000 $420 per repair*200 repairs+$10,000 = $94,000 © Dale R. Geiger
Demonstration Problem A vehicle repair shop incurs an average parts cost per repair of $220. Shop rent is $5,000 per month. Staff salaries are $5,000 per month and technicians earn a commission on repairs that averages $200 per repair. What is unit cost for 100 repairs? 200 repairs? Unit cost = Total cost / # repairs repairs $52,000 / 100 repairs = $520 repairs $94,000 / 200 repairs = $470 © Dale R. Geiger
Demonstration Problem A vehicle repair shop incurs an average parts cost per repair of $220. Shop rent is $5,000 per month. Staff salaries are $5,000 per month and technicians earn a commission on repairs that averages $200 per repair. What is unit cost for 100 repairs? 200 repairs? Unit cost = Total cost / # repairs repairs $52,000 / 100 repairs = $520 repairs $94,000 / 200 repairs = $470 © Dale R. Geiger
Demonstration Problem A vehicle repair shop incurs an average parts cost per repair of $220. Shop rent is $5,000 per month. Staff salaries are $5,000 per month and technicians earn a commission on repairs that averages $200 per repair. What is unit cost for 100 repairs? 200 repairs? Unit cost = Total cost / # repairs repairs $52,000 / 100 repairs = $520 repairs $94,000 / 200 repairs = $470 © Dale R. Geiger
Check on Learning What happens to total variable cost as number of units produced increases? What happens to unit fixed cost as number of units produced increases? © Dale R. Geiger
Practical Exercises © Dale R. Geiger